Modelling SFR-M* and M*-Z relations to be observed at

high-redshift with JWST

Emma Curtis-Lake & David Stenning Institute d’Astrophysique de Paris

Stephane Charlot, Jacopo Chevallard, Pratika Dayal, Julia Gutkin,

Michaela Hirschmann

NEOGAL

date 21/06/16

Motivation

Image credit: Harry Fergusonhttp://candels-collaboration.blogspot.fr/2013/02/star-formation-in-mountains.html

Stellar mass

SFR

Motivation

Stark+ 2013

Motivation

Pacifici+ 2014

Salmon+ 2015

Previous work

Kurczynski+ 2016

Previous work

Kurczynski+ 2016

Previous work

Question

How well can recover the intrinsic scatter from simulated, self-consistent star formation and chemical enrichment histories?

CF00 Dust attenuation

SFHs with known input M*-SFR relationshipSAM/Hydrodynamic simulation/toy model

BEAGLEmock catalogue

production

Stellar templates Chosen filter

profiles

Artificial photometry plus noise

BEAGLESED fitting

CF00 Dust attenuation

CF00 Dust attenuation

Charlot & Fall 2000

CF00 Dust attenuation

Charlot & Fall 2000

See Brett Salmon’s poster

BEAGLEmock catalogue

production

SFHs with known input M*-SFR relationshipSAM/Hydrodynamic simulation/toy model

CF00 Dust attenuation

Stellar templates Chosen filter

profiles

Artificial photometry plus noise

BEAGLESED fitting

BEAGLEmock catalogue

production

BEAGLEmock catalogue

production

•Includes self-consistent nebular emission based on wide grid of CLOUDY models - see Julia Gutkin’s poster!

SFHs with known input M*-SFR relationshipSAM/Hydrodynamic simulation/toy model

BEAGLEmock catalogue

productionCF00 Dust attenuation

Stellar templates Chosen filter

profiles

Artificial photometry plus noise

BEAGLESED fitting

BEAGLESED fitting

BEAGLESED fitting

At this stage we get to test impact of different fitting parameters on derivation of individual object physical parameters, as well as the M*-SFR relation as a whole.

Fitting parameters include:•Sampling of SED (different filter sets)•Depth of the data•Dust prescriptions•SFH prescriptions

measuring the M*-SFR relation

Notation

For galaxy i:

• SFRi is log10(SFR/M�yr�1

)

• Mi is log10(M?/M�)

• ⇥i are the remaining parameters (e.g., metallicity, z)

• yi are “observed” photometry, with known errors ⌃i

• µi = G(SFRi,Mi,⇥i) is predicted photometry from

forward-model G

First Level:

yi | SFRi,Mi,⇥i ⇠ N(µi,⌃i)

Second Level:

SFRi|Mi ⇠ �0 + �1Mi +N(0,�)Mi ⇠ Uniform(a, b)

measuring the M*-SFR relation

Multilevel model

First Level:

yi | SFRi,Mi,⇥i ⇠ N(µi,⌃i)

Second Level:

SFRi|Mi ⇠ �0 + �1Mi +N(0,�)Mi ⇠ Uniform(a, b)

P (SFR,M,⇥,�,�0,�1 | Y,⌃)

/ P (�)P (�0,�1)

NY

i=1

P (yi | SFRi,Mi,⇥i,⌃i)

⇥NY

i=1

P (SFRi | Mi,�0,�1,�)P (Mi)P (⇥i),

where SFR = (SFR1, . . . , SFRN ),M = (M1, . . . ,MN ),⇥ = (⇥1, . . . ,⇥N ),Y = (y1, . . . ,yN ),⌃ = (⌃1, . . . ,⌃N ), and N is the number of galaxies.

measuring the M*-SFR relation

Posterior Distribution

P (SFR,M,⇥,�,�0,�1 | Y,⌃)

/ P (�)P (�0,�1)

NY

i=1

P (yi | SFRi,Mi,⇥i,⌃i)

⇥NY

i=1

P (SFRi | Mi,�0,�1,�)P (Mi)P (⇥i),

where SFR = (SFR1, . . . , SFRN ),M = (M1, . . . ,MN ),⇥ = (⇥1, . . . ,⇥N ),Y = (y1, . . . ,yN ),⌃ = (⌃1, . . . ,⌃N ), and N is the number of galaxies.

measuring the M*-SFR relation

Posterior Distribution

Likelihood Function

P (SFR,M,⇥,�,�0,�1 | Y,⌃)

/ P (�)P (�0,�1)

NY

i=1

P (yi | SFRi,Mi,⇥i,⌃i)

⇥NY

i=1

P (SFRi | Mi,�0,�1,�)P (Mi)P (⇥i),

where SFR = (SFR1, . . . , SFRN ),M = (M1, . . . ,MN ),⇥ = (⇥1, . . . ,⇥N ),Y = (y1, . . . ,yN ),⌃ = (⌃1, . . . ,⌃N ), and N is the number of galaxies.

measuring the M*-SFR relation

Posterior Distribution

Likelihood Function

Prior Distribution

P (SFR,M,⇥,�,�0,�1 | Y,⌃)

/ P (�)P (�0,�1)

NY

i=1

P (yi | SFRi,Mi,⇥i,⌃i)

⇥NY

i=1

P (SFRi | Mi,�0,�1,�)P (Mi)P (⇥i),

where SFR = (SFR1, . . . , SFRN ),M = (M1, . . . ,MN ),⇥ = (⇥1, . . . ,⇥N ),Y = (y1, . . . ,yN ),⌃ = (⌃1, . . . ,⌃N ), and N is the number of galaxies.

measuring the M*-SFR relation

Posterior Distribution

Likelihood Function

Prior Distribution

Hyperprior

measuring the M*-SFR relation

measuring the M*-SFR relation

P (SFR,M,⇥,�,�0,�1 | Y,⌃)

/ P (�)P (�0,�1)

NY

i=1

P (yi | SFRi,Mi,⇥i,⌃i)

⇥NY

i=1

P (SFRi | Mi,�0,�1,�)P (Mi)P (⇥i),

where SFR = (SFR1, . . . , SFRN ),M = (M1, . . . ,MN ),⇥ = (⇥1, . . . ,⇥N ),Y = (y1, . . . ,yN ),⌃ = (⌃1, . . . ,⌃N ), and N is the number of galaxies.

measuring the M*-SFR relation

Posterior Distribution

Test scenario

Test scenarioInput:Constant SFHs drawn from M*-SFR relation with known parameters (intercept, slope and scatter).•No Dust•Single metallicity•Single Redshift•Including nebular emission•CANDELS Deep depths/filters + IRAC CH1 + CH2

SED Fitting:•Constant SFHs•No Dust•Redshift left free•Metallicity left free

Test:•Can we recover the input M*-SFR relation parameters?

Test scenario

6 7 8 9 10 11 12

log(Mass /M�)

�1.0

�0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

log(

SFR

/M�

yr�

1)

6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0 10.5

log10 (M⇤ /M�)

�1.0

�0.5

0.0

0.5

1.0

1.5

2.0

2.5

log 1

0(S

FR

/M�

yr�

1)

0.0 0.5 1.0 1.5 2.0 2.5 3.0

log(SFR in)

0.0

0.5

1.0

1.5

2.0

2.5

3.0

log(

SFR

mea

sure

d)

8.0 8.5 9.0 9.5 10.0 10.5

log(Mass in)

7.5

8.0

8.5

9.0

9.5

10.0

10.5

log(

Mas

sm

easu

red)

8.0 8.5 9.0 9.5 10.0 10.5

log(Mass in)

7.5

8.0

8.5

9.0

9.5

10.0

10.5

log(

Mas

sm

easu

red)

6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0 10.5

log10 (M⇤ /M�)

�1.0

�0.5

0.0

0.5

1.0

1.5

2.0

2.5

log 1

0(S

FR

/M�

yr�

1)

6 7 8 9 10 11 12

log(Mass /M�)

�1.0

�0.5

0.0

0.5

1.0

1.5

2.0

2.5

log(

SFR

/M�

yr�

1)

8.0 8.5 9.0 9.5 10.0 10.5

0.5

1.0

1.5

2.0

mass

SFR

Test scenario

log10(M* / M☉)

log 1

0(SFR

/ M

☉yr

-1)

8.0 8.5 9.0 9.5 10.0 10.5

0.5

1.0

1.5

2.0

mass

SFR

Test scenario

log10(M* / M☉)

log 1

0(SFR

/ M

☉yr

-1)

8.0 8.5 9.0 9.5 10.0 10.5

0.5

1.0

1.5

2.0

mass

SFR

8.0 8.5 9.0 9.5 10.0 10.5

0.5

1.0

1.5

2.0

mass

SFR

β0 (intercept) β1 (slope) σ (intrinsic scatter)Β0

Density

−6 −4 −2 0 2

0.0

0.1

0.2

0.3

0.4

Β1

Density

0.0 0.2 0.4 0.6

01

23

σ

Density

0.25 0.35 0.45 0.55

02

46

810

Test scenario

log10(M* / M☉)

log 1

0(SFR

/ M

☉yr

-1)

8.0 8.5 9.0 9.5 10.0 10.5

0.5

1.0

1.5

2.0

mass

SFR

8.0 8.5 9.0 9.5 10.0 10.5

0.5

1.0

1.5

2.0

mass

SFR

β0 (intercept) β1 (slope) σ (intrinsic scatter)Β0

Density

−6 −4 −2 0 2

0.0

0.1

0.2

0.3

0.4

Β1

Density

0.0 0.2 0.4 0.6

01

23

σ

Density

0.25 0.35 0.45 0.55

02

46

810

Test scenario

log10(M* / M☉)

log 1

0(SFR

/ M

☉yr

-1)

8.0 8.5 9.0 9.5 10.0 10.5

0.5

1.0

1.5

2.0

mass

SFR

8.0 8.5 9.0 9.5 10.0 10.5

0.5

1.0

1.5

2.0

mass

SFR

β0 (intercept) β1 (slope) σ (intrinsic scatter)Β0

Density

−6 −4 −2 0 2

0.0

0.1

0.2

0.3

0.4

Β1

Density

0.0 0.2 0.4 0.6

01

23

σ

Density

0.25 0.35 0.45 0.55

02

46

810

Test scenario

log10(M* / M☉)

log 1

0(SFR

/ M

☉yr

-1)

8.0 8.5 9.0 9.5 10.0 10.5

0.5

1.0

1.5

2.0

mass

SFR

Summary

BEAGLE allows us to both produce mock photometry with self-consistent SF and chemical enrichment histories and nebular emission as well as performing full Bayesian SED fitting (see Jacopo Chevallard’s talk and Julia Gutkin’s poster).

Our Bayesian Hierarchical modelling can recover and provide the full uncertainties in slope, intercept and intrinsic scatter of the M*-SFR relation.

•No assumption of shape of joint uncertainties in M*-SFR for individual objects.

•Allows us to assess and compare different selection and SED fitting strategies.

For more results - see my talk at the Malta “Signals from the Deep Past” conference